Warning her party against taking victory for granted, she said a Goldsmith campaign could attract enough Green supporters and Liberal Democrats to win on second preferences.

Writing in ProgressOnline, Ms Kober said Labour could not win by appealing only to core supporters. She went on: “We also need a Labour candidate who can beat Zac Goldsmith (should he be persuaded to enter the race) because he is without question the greatest potential obstacle to Labour winning City Hall.

“This year he was returned to parliament with a majority of 23,000 in a seat that was held for many years by the Liberal Democrats.

“I fear his appeal is likely to stretch beyond west London and that he will pick up Liberal Democrat and Green second preferences across the capital.”

Mr Goldsmith could become a huge headache for David Cameron if he runs because of his forthright opposition to Heathrow expansion. He has threatened to force a by-election if the Prime Minister tries to give a go ahead to a third runway after the Airports Commission reports next month.

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The Evening Standard revealed last August that Boris Johnson was pressing the Richmond Park MP to run as his successor next May.

The pair have campaigned together against the Third Runway and are good friends. At first Mr Goldsmith did not rule it out — but later appeared to shut the door on the idea, saying he wanted to continue as an MP.

But a poll in December found he was the only likely Tory candidate who was well-known to Londoners, and last month Green peer Baroness Jenny Jones said many Greens would probably prefer him to a Labour rival.

Bookmakers Ladbroke last night slashed the odds on him becoming Conservative candidate, making him the hot favourite even though he has not yet agreed to stand.

Ladbrokes said there had been “a flurry of bets” online and in betting shops in South and East London on Tuesday, totalling seveal thousand pounds.

The sudden activity caused his odds crash in an hour from 7/4 to evens.

Spokesman Matthew Shaddick said: “Whilst Zac has given no indication of any Mayoral ambitions, the money clearly suggests that he’s the man who might keep City Hall in Tory hands again.”

The 2016 contest has long been seen as Labour’s to lose. But with the Greens and Ukip far stronger than in the last contest in 2012, second preferences will be more vital than ever.

Ms Kober said it was complacent to assume “London is a Labour city” and argued: “We need a candidate who is not simply tribally Labour.”

Senior Labour MP Jon Cruddas urged Labour in an Evening Standard interview yesterday to take seriously the risk of losing City Hall again.